---
name: "dpbcon.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/dpbcon.f"
---

# dpbcon.f(3)

## NAME

SRC/dpbcon.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dpbcon** (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork, info)\
 **DPBCON**

## Function/Subroutine Documentation

### subroutine dpbcon (character uplo, integer n, integer kd, double precision, dimension( ldab, \* ) ab, integer ldab, double precision anorm, double precision rcond, double precision, dimension( \* ) work, integer, dimension( \* ) iwork, integer info)

**DPBCON**

**Purpose:**

```
!>
!> DPBCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a real symmetric positive definite band matrix using the
!> Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangular factor stored in AB;
!>          = 'L':  Lower triangular factor stored in AB.
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*KD*

```
!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
!>
```

*AB*

```
!>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**T*U or A = L*L**T of the band matrix A, stored in the
!>          first KD+1 rows of the array.  The j-th column of U or L is
!>          stored in the j-th column of the array AB as follows:
!>          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
!>
```

*LDAB*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+1.
!>
```

*ANORM*

```
!>          ANORM is DOUBLE PRECISION
!>          The 1-norm (or infinity-norm) of the symmetric band matrix A.
!>
```

*RCOND*

```
!>          RCOND is DOUBLE PRECISION
!>          The reciprocal of the condition number of the matrix A,
!>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
!>          estimate of the 1-norm of inv(A) computed in this routine.
!>
```

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (3*N)
!>
```

*IWORK*

```
!>          IWORK is INTEGER array, dimension (N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **130** of file **dpbcon.f**.

## Author

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